Several models of random manifolds and random simplicial complexes were suggested and studied recently, see [1]} for a survey.
One may mention random surfaces [2]}, random 3-manifodls
[3]}, random configuration spaces of linkages [4]}.
The present paper is was inspired by
the model of random simplicial complexes developed by Linial, Meshulam and Wallach [5]} , [6]}.
In the first paper [5]} the authors
studied an analogue of the classical Erdös - Rényi [8]} model of random graphs in the situation of 2-dimensional simplicial complexes. In the following paper
[6]}
a more general model of \(d\) -dimensional
random simplicial complexes was studied. The random simplicial complexes of [5]} and [6]} have the complete \((d-1)\) -skeleton and their “randomness is concentrated in the top dimension”.
More specifically, one starts with the full \((d-1)\) -skeleton of an \((n-1)\) -dimensional simplex and adds \(d\) -faces at random, independently of each other, with probability \(p\) .
